Experiment 3 - Printed Filters.

Transcription

1 Experiment 3 - Printed Filters. S. Levy, Z. Ibragimov, D. Ackerman and H. Matzner. May 3, 2009 Contents 1 Background Theory EllipticFilterDesign ImpedanceandFrequencyScaling Example Solution PrintedFilterTheory Example Solution Experiment Procedure Lumped Elements Elliptic LPF Design Simulation Measurement ADSSimulationofaPrintedLPF CSTSimulationofaPrintedLPF MeasurementofaPrintedLPF c 1

2 1 Background Theory 1.1 Elliptic Filter Design A prototype of a third order Elliptic LPF with the element values for the normalized lowpass function, is shown in Figure 1. L 2 R s =1 Ω C 2 AC C 1 C 3 R L =1 Ω Figure 1 - A prototype of a third order Elliptic LPF. A sample section table for the prototype element values for the normalized lowpass function of order 3, which assumes a cutoff frequency of 1 rad sec source and load impedances of 1 Ω, is presented in Table 1. θ A min C 1 = C 3 C 2 L Table 1: Section table for elements values for an Elliptic LPF, N=3. Where θ is calculated by: µ θ =sin 1 ωc ω s 2

3 Where ω s is the stopband frequency in rad, ω sec c is the cutoff frequency in rad,anda sec min is the minimum stopband attenuation in db (see Figure 2). Figure 2 - Magnitude response of a third order Elliptic LPF Impedance and Frequency Scaling The elements from the table of the LPF are normalized by frequency and impedance. For different frequency and impedance, elements can be obtained by the impedance and frequency transformation: C 0 k = C k Z 0 ω c L 0 k = L kz 0 ω c Where C k and L k are the normalized elements values from the tables, C is the denormalized (actual) capacitor value, L is the denormalized (actual) inductor value, and R is the final load resistor Example Design an elliptic LPF, f 0 =5MHz, N =3and at least 30 db stopband attenuation at 11 MHz. Calculate the values of the capacitors and inductors, assume that Z in = Z Load =50Ω. 3

4 1.1.3 Solution µ µ θ =sin 1 ωc 5 =sin 1 = ω s 11 From Table 3, we can see that C 1 = C 3 = , C 2 = and L 2 = For Z 0 =50Ω and ω c =2π = rad, we can scale the sec elements as: C1 0 = C3 0 = C 1 Z 0 ω c = = pf C2 0 = C 2 Z 0 ω c = = pf L 0 2 = L 2Z 0 ω c = =1.587 μh TheschematiccircuitfortheLPFisshowninFigure3. L 2 = 1.587μH R s =50 Ω C 2 =101.41pF AC C 1 = pF C 3 =685.83pF R L = 50 Ω Figure 3 - A schematic circuit for the elliptic LPF. The graph of S 21 and S 11 in db as a function of frequency is shown in Figure 4. 4

5 db(s(1,1)) db(s(2,1)) m1-20 indep(m1)= 1.100E7 plot_vs(db(s(2,1)), freq)= m freq, MHz Figure 4 - The graph of S 21 and S 11 in db of the Elliptic LPF. 1.2 Printed Filter Theory Higher frequency filters are implemented by transmission line sections instead of the lumped elements. Richard s transformations enable us to replace a lumped element by a shorted or opened transmission line sections, as shown in Figure 5. 5

6 Figure 5 - Richard s transformations Kuroda identities help to separate transmission line stubs, transform series stubs into shunt stubs, or vice versa or change impractical characteristic impedances into more realizable ones, as shown in Figure 6. 6

7 Figure 6 - Kuroda s Identities Example Design a 3 rd order low-pass Chebyshev 3 db microstrip filter for 4 GHz cutoff frequency Solution 1. Starting from the low-pass normalized filter: g 1 = = L 1, g 2 = = C 1, g 1 = = L 3, g 4 = 1.0 =R L, The normalized lumped element filter is shown in Figure 7. 7

8 Figure 7 - A normalizeed 3 rd order Chebyshev 3 db ripple lumped filter. 2. Replace the lumped elements by open/short loaded transmission line sections by using Richards s transformations, as shown in Figure 8. Figure 8 - The lumped elements were replaced by transmission line section by using Richard s transformations. 3. Next, we will separate the transmission line stubs. As a first step, we will add two unit characteristic impedance sections of length l ("unit elements") to the left and to the right of the center structure, as shown in Figure 9. This addition do not change the performance of the circuit. 8

9 Figure 9 - Unit elements were added to the center of the structure. 4. Now we will move the unit elements between the stubs by using the second Kuroda identity looking to the right part of the circuit (the same is for the left side), as shown in Figure 10. Figure 10 - Kuroda s 2nd identitiy Z 1 = Z 2 =1 9

10 n 2 =1+Z 2 /Z 1 =1+1/ = n 2 Z 1 = = 4.35 n 2 Z 2 =1.299 We will get a new circuit, as shown in Figure 11. Figure 11 - Insert transmission line sections between the stubs. 5. In the last stage, we will multiply each characteristic impedance by 50 Ω and change the length to λ/8 of the cutoff frequency, as shown in Figure

11 Figure 12 - The final transmission lines filter. 6. Now we can design the filter with microstrip transmission line sections, as shown in Figure 13. Figure 13 - The microstrip filter. The length of each stub will be: l = 1 8 λ εeff = c 8 f ε eff 11

12 2 Experiment Procedure 2.1 Lumped Elements Elliptic LPF Design 1. Design an elliptic LPF, f 0 =1.9MHz, N =3and at least 28 db stopband attenuation at 4 MHz. Calculate the values of the capacitors and inductors, assume that Z in = Z Load =50Ω Simulation Verify your design by simulation using ADS software (only the lumped elements), as shown in Figure 1. S-PARAMETERS L L1 L= S_Param SP1 Start=300 khz Stop=10 MHz Step=0.5 MHz P_AC PORT1 Num=1 Z=50 Ohm Pac=polar(dbmtow (0),0) Freq=freq C C1 C= C C2 C= C C3 C= Term Term2 Num=2 Z=50 Ohm Figure 1 - ADS layout for the Elliptic LPF lumped elements prototype. Draw the graphs of S 21 (Magnitude, and phase), S 11 (Magnitude only),s 22 (Magnitude only) of the filter in the frequency range of 300 khz 10 MHz Measurement 3. Connect the microstrip LPF MHz to the network analyzer with a coaxial cable and measure S 21 (Magnitude and phase), S 11 (Magnitude only),s 22 (Magnitude only) of the filter in the frequency range to 300 khz 10 MHz. 12

13 4. Exchange the microstrip LPF with the coaxial LPF (Mini-Circuits BLP-1.9) and measure S 21 (Magnitude and phase), S 11 (Magnitude only),s 22 (Magnitude only) of the filter. 5. Compare the graphs from paragraph 4 to the graphs from paragraph ADS Simulation of a Printed LPF 1. Construct an ADS simulation of the microstrip low-pass filter from the Background Theory section, by ideal transmission lines, as shown in Figure 2. S-PARAMETERS S_Param SP1 Start=0.5 GHz Stop=10.0 GHz Step=100 MHz TLIN TL1 Z=50.0 Ohm E=45 F=4 GHz Term Term1 Num=1 Z=50 Ohm Ref TLIN TL3 Z=217.5 Ohm E=45 F=4 GHz TLOC TL10 Z=64.9 Ohm E=45 F=4 GHz Ref TLIN TL2 Z=217.5 Ohm E=45 F=4 GHz TLOC TL9 Z=70.3 Ohm E=45 F=4 GHz Ref TLIN TL7 Z=50.0 Ohm E=45 F=4 GHz TLOC TL11 Z=64.9 Ohm E=45 F=4 GHz Term Term2 Num=2 Z=50 Ohm Figure 2 - The filter constructed from ideal transmission lines. Plot the graphs of S 11 and S 21 (Magnitude and phase) in the frequency range 500 MHz 10 GHz. 2. Construct an ADS simulation of the microstrip low-pass filter from the Background Theory section, on a substrate FR4 with a permittivity of 13

14 ε r =4.9, height of substrate is h =1.6 mm, height of conductive layer is T =0.02 mm and a loss tangent of tan δ =0.018, asshowninfigure3. MSub MSUB MSub1 H=1.6 mm Er=4.9 Mur=1 Cond=1.0E+50 Hu=1.0e+033 mm T=0.02 mm TanD= Rough=0 mm S-PARAMETERS S_Param SP1 Start=0.5 GHz Stop=10.0 GHz Step=100 MHz MLIN TL1 Subst="MSub1" W= Term L= Term1 Num=1 Z=50 Ohm MLIN TL2 Subst="MSub1" W= MLIN L= TL5 Subst="MSub1" W= L= R R1 R=9999 MOhm MLIN TL3 Subst="MSub1" W= MLIN L= TL6 Subst="MSub1" W= L= R R2 R=9999 MOhm MLIN TL4 Subst="MSub1" W= MLIN L= TL7 Subst="MSub1" W= L= R R3 R=9999 MOhm Term Term2 Num=2 Z=50 Ohm Figure 3 - The filter constructed from microstrip transmission lines. For calculating the dimensions of the total strip, use ADS s LineCalc or CST s Macros Calculate Calculate analytical Line Impedance for calculating the width (w) and ε eff of each strip, as shown in Figure 4. 14

15 Figure 4 - Finding w and ε eff of each strip. Plot the graphs of S 11 and S 21 (Magnitude and phase) in the frequency range 500 MHz 10 GHz. 3. Compare the graphs for the ideal and microstrip transmission lines filters. 2.3 CST Simulation of a Printed LPF Construct a CST simulation of the microstrip low-pass filter from the Background Theory section. Choose the "Filter (Planar, Microstrip, cpw)" template. Use the extrude function, for the construction of the total strip. Define two waveguide ports. The final model of the LPF should similar to Figure 5. 15

16 Figure 5 - The final model for the LPF. Set the frequency range to 0 7 GHz and start the simulation for only port 1 and mode 1. Plot the graphs of S 11 and S 21 (Magnitude and phase). 2.4 Measurement of a Printed LPF Connect a microstrip filter to the network analyzer and observe its S 11 and S 21 (Magnitude and phase). 16